Similarity relations on finite ordered sets
โ Scribed by D.G Rogers
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 507 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Watanabe, M., Arrow relations on families of finite sets, Discrete Mathematics 94 (1991) 53-64. Let n, m and k be positive integers. Let X be a set of cardinality n, and let 9 be a family of subsets of X. We write (n, m)-, (n -1, mk), when for all 9 with (S( em, there exists an element x of X such t
Abstmct# A decomposition is given for fini\*.e ordered sets P and is shown to bc a unique decomposition in the sense of Brylawski. Hence there exists a universal invariant g(P) for this decomposition, and we c(Dmpute g(P) explicitly. Some modifications of this decomposition are considered; in partic
A simple proof is given for the fact that the number of nonsingular similarity relations on (1,2,... n), for which the transitive closure consists of k blocks, equals ("\*;'\_i-') -(2"-fh -'), 1, =G k s n/2. In particular, this implies a recent result of Shapiro about Catalan numbers and Fine's Jequ
In this paper, we consider the following Ramsey theoretic problem for finite ordered sets: For each II 3 1, what is the least integer f(n) so that for every ordered set P of width it, there exists an ordered set Q of width f(n) such that every 2-coloring of the points of Q produces a monochromatic